Five Massive Contact Binaries with Twin Components in LMC

In order to acquire profound insights into the evolutionary processes of stars, it is of utmost importance to meticulously observe and accurately determine their parameters within the Local Group. Eclipsing binaries (EBs) provide an ideal platform for achieving this goal through the careful analysis of their light curves and spectra. The massive binary is attractive because of its plethora of physical processes and astrophysical phenomena, such as gravitational waves (Schneider et al. 2001), X-ray binaries (Verbunt 1993), gamma-ray bursts (Izzard et al. 2004), and so on. Recent studies have shown that a notable fraction of star forms as constituents of binary or multiple star systems (Kratter 2012). Sana et al. (2012) found that over 70% of massive stars exchange mass with their companions via Roche lobe overflow, and this strong interaction distinguishes them from single stars. In addition, Moe & Di Stefano (2017) and Offner et al. (2023) summarized the results of observational and theoretical studies of stellar multiplicity, showing that over 35% of OB stars belong to triple or higher-order systems and that the fraction increases with the component mass of the binary. The comprehensive study of massive binaries will shed new light on their formation and evolution. In particular, twin binaries (where the mass ratios range from 0.9 to 1) receive special attention because they are so intriguing and deserve to be studied more fully.

For twin binaries, Pinsonneault & Stanek (2006) and Cantrell & Dougan (2014) have proposed that their evolution is qualitatively different from that of binaries with components of quite different masses. Lucy (2006) and Simon & Obbie (2009) preliminarily displayed the proportion of the late spectral type (F, G, and K) twins. Subsequently, Moe & Di Stefano (2017) and Offner et al. (2023) delved into the study of twin binaries, focusing on the measurement of the fraction of early-type binaries characterized by short orbital periods. They got a lower twin fraction among O-type and early-B twins (∼10%) compared to solar-type binaries (∼30%) and proposed that the twin components coevolved via Roche lobe overflow and/or shared accretion in the circumbinary disk. Tokovinin & Moe (2020) discussed how accretion-driven migration can lead to short-period twins. Sana et al. (2012) and Offner et al. (2023) noted that there are no twin binaries among O-type and early B-type binaries when the binary semimajor axis exceeds 0.5 au. Several detailed studies have contributed to the understanding of twin binaries. Notably, Hwang et al. (2022) provided evidence for the formation of twin binaries by analyzing the eccentricity of wide twin binaries. Additionally, Bulut et al. (2021) and Yücel & Bakış (2022) presented a series of twin-component parameters based on the Kepler EB light curves. However, these studies mainly focused on late-type and detached twin binaries, and there remains a paucity of literature for early-type twin contact binaries, which primarily include certain contact massive twins that are within the Galaxies or galaxies, such as CT Tau, GU Mon and V701 Sco (Yang et al. 2019), V593 Cen (Zhao et al. 2019), VFTS 352 (Almeida et al. 2015), HD 64315 (Lorenzo et al. 2017), and M31V J00450522+4138462 (Li et al. 2022b). These works discussed the formation and evolution of massive twin binaries by the parameters of spectra and photometry and tried to understand the transfer or loss of mass and angular momentum between companions; MacLeod & Loeb (2020) studied the influence of stellar winds on these processes for twins. Moreover, massive stars have a weakness of the stellar winds at low metallicity (Yoon & Langer 2005). Consequently, studying the Large Magellanic Cloud (LMC) in a different environment, searching for relevant celestial bodies, and conducting in-depth exploration can provide further evidence and insights into the formation and evolution of massive twin binaries.

It is known that the metallicity in the LMC is lower than that in the Milky Way (Choudhury et al. 2016), which may affect stellar evolution (Westerlund 1997). Menon et al. (2021) presented models for the formation of close contact pairs for LMC and Small Magellanic Cloud (SMC) metallicities, and they showed that most should evolve toward equal-mass pairs. Through extensive photometric surveys conducted by projects such as the MAssive Compact Halo Objects (MACHOs; Alcock et al. 1996) and the Optical Gravitational Lensing Experiment (OGLE; Graczyk et al. 2011; Pawlak et al. 2016), thousands of EBs have been discovered in the LMC. Pawlak et al. (2016) collected 40,204 EBs in LMC from the fourth phase of the OGLE project, which contains 497 contact binary candidates in this catalog. In this study, our first step is to identify these twin binaries, which will provide us with the fundamental parameters of the contact binaries. Subsequently, we construct and analyze the orbital periods of the twin binaries for the first time, aiming to identify the presence of third bodies orbiting the central twin binaries and elucidate their role in the formation and evolution of the twin binaries. These twin binaries, which represent a unique class of binary systems at a particular stage of evolution, provide a valuable opportunity to explore the evolution of massive binaries and to test evolutionary models. The subsequent sections of the paper are organized as follows: Section 2 describes the data acquisition process, Section 3 presents a detailed analysis of the orbital period variations, Section 4 focuses on the determination of the physical parameters, and Section 5 provides in-depth discussions and conclusions.

All the light curves used in this study were obtained from the OGLE ⁵ and MACHO ⁶ databases, and the photometric reduction methods are described in detail in the literature (Alcock et al. 1996; Graczyk et al. 2011; Pawlak et al. 2016). While most of the data used in this study come from the OGLE project, it is worth noting that the contributions from the MACHO project are also significant, especially for time-series photometry. The OGLE is a long-term variability sky survey project that was initiated in 1992 by the University of Warsaw, which includes the targets in the LMC. The fourth phase of the OGLE project (OGLE IV) utilizes a 32-chip mosaic CCD camera with a 15 field of view (Udalski et al. 2015), and this telescope (1.3 m), equipped with V and I band filters, produces high-quality data. These data were observed with the I- and V-band filters, with about 90% taken in the I band, and those of the I and V (enough data) bands were used to calculate photometric solutions in this work. The telescope (1.3 m) was equipped with an 8-chip mosaic camera, with a field of view of about 35' × 35' in the OGLE III phase. Data from OGLE IV and III were used to obtain the eclipse times (or minima), and data from the MACHO project were also used to obtain the minima to extend the time span of the eclipse times as those from OGLE I and OGLE II are not available during this period. MACHO built a two-channel system that employs eight 2048 × 2048 CCDs, mounted on the 50 inch telescope with two bands (Alcock et al. 1996) at the Mount Stromlo observatory.

The identification of the twin massive contact binaries consists of a series of steps. First, the catalog of contact binaries from Pawlak et al. (2016) was used as a starting point, which initially contained 497 contact binaries. Second, the selection criteria focused on identifying systems that exhibited characteristics indicative of a massive binary (i.e., spectral type earlier than B5V after considering reddening) with a color index of V − I below −0.07. This filtering process resulted in 46 systems being retained. Third, systems with primary and secondary minima depths less than 0.1 mag were eliminated, resulting in the exclusion of seven binaries. Finally, fundamental parameters and geometric configurations were determined using the Wilson and Devinney (W-D) software program (Wilson & Devinney 1971; Wilson 1990, 2012; van Hamme & Wilson 2003; Wilson & Wyithe 2003). As a result, a total of 32 massive contact binaries were identified, out of which five were confirmed as massive twin contact binaries. The details can be found in Table 1, with the basic information sourced from Pawlak et al. (2016) and the E(V − I) values provided by Skowron et al. (2021). Note that all systems in this study have periods of less than 1 day. For convenience, all of the systems are referred to as SXXXXX from the initial name of OGLE LMC-ECL-XXXXX in this work.

Table 1. The Basic Information of the Five Binaries

Parameters	S02776	S12878	S15994	S18865	S19959
Period (day)	0.524973	0.7960623	0.6769579	0.5952488	0.7504953
Epoch (HJD–2,450,000)	7000.1023	7000.0394	7000.4096	7000.4556	7000.0902
I (mag)	17.987	15.798	15.756	17.461	16.446
V (mag)	17.917	15.713	15.608	17.354	16.355
V − I (mag)	−0.07	−0.085	−0.148	−0.107	−0.091
E(V − I) (mag)	0.086	0.105	0.116	0.069	0.144
(V − I)0 (mag)	−0.156	−0.19	−0.264	−0.176	−0.235
${T}_{{(V-I)}_{0}}$ (K)	15,200	17,000	23,200	16,400	21,000
TGaia (K)	10,000	16,900	16,875	15,066	17,178
${T}_{{M}_{v}}$ (K)	17,000	21,870	23,430	18,500	23,140

Download table as:  ASCIITypeset image

In the case of early-type binaries, the phenomenon known as the light travel time effect (LTTE) presents a fruitful approach for detecting tertiary bodies, which is based on the gravitational influence of the additional body. The mathematical formulation for the LTTE could refer to Hajdu et al. (2019), and this theory has gained widespread acceptance. To find the third body for these five massive binaries, the LTTE was adopted. In this process, the observed minima are needed for these binaries; then, the theoretical minima are subtracted from the observed minima, resulting in the quantities referred to as O − C (Qian et al. 2013; Li et al. 2021; Wang et al. 2022). The periodic oscillations in the O − C values indicate the possible presence of a third body influencing the binary system.

The OGLE and MACHO surveys do not provide continuous observations, making direct detection of minima infeasible. To address this, we have adopted a method of obtaining the minimum using data from several periods. All data (OGLE III, OGLE IV, MACHO) were utilized, with the exception of S02776 and S15994, which were not observed in the MACHO project. We employed 120 data points to determine the primary and secondary minima by converting the time-series data to phase by fitting a parabola (as illustrated in Figure 1). Then 50 data points were shifted to determine the subsequent minimum. All the primary and secondary eclipses of five twin binaries are listed in Table 4 of the Appendix. This method was demonstrated and adopted by many authors (Liu et al. 2015; Shi et al. 2021; Li et al. 2022c) and has proven useful for analyzing period variations in EBs with long-term observational data. This method is also similar to the AFP method used by Zasche et al. (2014), which has led to the discovery of many hierarchical triple system candidates in the Galactic Bulge (Hajdu et al. 2019) and SMC (Zasche et al. 2017). However, because of the temporal smoothing associated with the measurement of the minima, the smoothed result has an amplitude that is smaller than actual, and the parameters derived from the amplitude may be slightly underestimated.

Zoom In Zoom Out Reset image size

The next step is to construct the O − C curves for these twins after deriving the corresponding minima. The linear ephemerides have been provided by Pawlak et al. (2016), and the detailed values are listed in Table 1. The time span of the obtained minima is approximately 10 yr for S02776 and S15994 due to the lack of MACHO data, while it is about 20.1 yr for the remaining binaries. The O − C curves are shown in the upper panel of Figure 2, and the primary minima are determined by the epoch listed in Table 1. The O − C curves clearly exhibit cyclic oscillations characterized by either parabolic or linear variations in the case of all five twin binaries. It is noteworthy that, except for S02776, the parabolic fit yields a smaller ${\chi }_{\nu }^{2}$ value in comparison to the linear fit. Furthermore, a circular orbit adequately describes the orbital motion of all binaries. Nevertheless, it should be addressed that some other process (magnetic activity and mass motions) might cause eclipse timing variations. However, magnetic activity is only common in late-type stars, so a cyclic oscillation caused from a third body by the LTTE is a reasonable explanation for these massive binaries. It is noted that the least-squares fit with weights of the errors was used in fitting the curves, and the following formula was used to calculate the detailed parameters:

$$\begin{eqnarray}&&O-C={\rm{\Delta }}{T}_{0}+{\rm{\Delta }}{P}_{0}\times E+\beta \times {E}^{2}+\tau ,\end{eqnarray} \tag{ 1 }$$

where E represents the epoch number, β denotes the rate of the linear period increase, ΔT₀ and ΔP₀ refer to the revised epoch and period respectively, τ refers to the cyclic modulation term caused by the LTTE, and the term of τ refers to the sinusoidal function for these five twin binaries. The orbital parameters and the revised values are listed in Table 2, where $\dot{P}$ is the rate of periodic change of binary stars, f(m) is the mass function of the systems with a third body, and A is semi-amplitude. ${M}_{3}\sin {i}_{3}$ is the mass of the third body, which is based upon the binary mass estimated from the mass ratio and the color-based primary star mass. D_max is the maximum distance between the third body and binary system, which is based upon Kepler's third law, the measured P₃, and estimated total mass. The time span of all binaries is more than one complete oscillation period except for S02776, which indicates that the cyclic modulation is much more reliable. Most binaries have a positive $\dot{P}$.

Zoom In Zoom Out Reset image size

Table 2. Orbital Parameters of the Third Body for Five Massive Binaries

Parameters	S02776	S12878	S15994	S18865	S19959
ΔT0 (day) × 10−3	−3.7(±4.1)	−10.9(±1.1)	22.2(±0.7)	1.8(±0.5)	16.7(±0.6)
ΔP0 (day) × 10−6	2.15(±0.19)	−7.07(±0.47)	15.01(±0.33)	−0.11(±0.15)	10.34(±0.22)
A (day) × 10−3	6.2(±2.2)	2.4(±0.2)	1.5(±0.1)	1.8(±0.3)	3.5(±0.2)
P3 (yr)	12.03(±0.42)	11.22(±0.64)	5.03(±0.15)	9.45(±0.36)	4.34(±0.03)
$\dot{P}(\mathrm{day}\,{\mathrm{yr}}^{-1})\times {10}^{-7}$	0	−1.05(±0.41)	14.8(±0.4)	0.17(±0.12)	1.43(±0.18)
f(m) (M⊙)	0.0085	0.0006	0.0007	0.0003	0.0118
${a}_{12}\sin {i}_{3}$ (au)	1.071(±0.380)	0.415(±0.035)	0.259(±0.017)	0.311(±0.052)	0.605(±0.035)
${M}_{3}\sin {i}_{3}$ (M⊙)	0.96(±0.26)	0.42(±0.06)	0.62(±0.05)	0.33(±0.04)	1.46(±0.05)
Dmax (au)	11.4	10.8	7.7	9.7	6.7

Download table as:  ASCIITypeset image

The light curves serve as crucial observational data for exploring the Universe and providing valuable information. Using a reliable tool is essential to extract meaningful insights from these observations. In this regard, the W-D program proves to be instrumental in determining fundamental parameters of binaries, including masses, radii, and orbital inclination. The W-D program was first published in 1971 and has been continuously developed and improved over four decades. The 2013 version was used for parameter determination in this study. The primary components' temperatures of these twin binaries are to be estimated based on available observations as our initial task. Since we lack spectral data, the V − I color index makes a great contribution to this work. The magnitude values of V and I bands were provided by Pawlak et al. (2016), then the values of (V − I)₀ were carried out after accounting for the reddening map (Skowron et al. 2021), which help us estimate the first group candidate temperatures (${T}_{{(V-I)}_{0}}$) via the online table ⁷ by Mamajek (based mainly on Table 5 from Pecaut & Mamajek 2013). To ascertain more reliable temperatures for these binaries, we attempted to obtain their temperatures through other means. Temperature values (T_Gaia) were collected from Gaia Collaboration (2022). Meanwhile, temperature $({T}_{{M}_{v}})$ was calculated using M_v from a contact binary relation (period–luminosity–color) in the LMC given by Pawlak (2016), with the following formula:

$$\begin{eqnarray}\begin{array}{rcl}{M}_{V} & = & -3.47{(\pm 0.87)\mathrm{log}P+7.57(\pm 1.21)(V-I)}_{0}\\ & & -0.97(\pm 0.26).\end{array}\end{eqnarray} \tag{ 2 }$$

Ultimately, we selected ${T}_{{(V-I)}_{0}}$ as the temperature of the primary star of twin binaries as its value falls within the range of the other two sets of values. These temperatures are listed in Table 1.

In the analysis performed with the W-D program, it would have been ideal to utilize multiband data for a more reliable solution. However, due to limited data in the V band, only the light curve in the I band was available for three of the binaries (S02776, S12878, and S15994). The temperatures of these binaries indicate that they have B-type spectral classifications. Consequently, the bolometric albedos A₁ = A₂ = 1.0 (Ruciński 1969) and the gravity-darkening coefficients g₁ = g₂ = 1.0 (Lucy 1967) were adopted. In the W-D program, star 1 represents the component that is eclipsed when the system undergoes a primary eclipse. The bolometric and bandpass limb-darkening coefficients were determined according to the logarithmic function. The next step was to select a suitable mode (mode 3 for contact binaries or others) for these contact binary candidates. By comparison with other modes, we confirmed that both components of these binaries fill their Roche lobes; thus they were demonstrated as contact binaries. To carry out a convergent solution, the following detailed configuration was implemented: the orbital inclination i, the modified dimensionless surface potential of star 1 (Ω₁), the effective surface temperature of star 2 (T₂), and the bandpass luminosity of star 1 (L₁) are set as free parameters, while T₁ and other parameters are fixed. The subsequent task is to determine the preliminary mass ratio (M₂/M₁). We employed the q-search method (Zhang et al. 2017; Liu & Li 2021; Wang & Zhu 2021) to accomplish this. The results of the q-search are shown in Figure 3, where (a) and (b) illustrate the lowest residuals near a mass ratio of 1 and (b) specifically represents the q-search for S19959, which demonstrates that the results of the q-search obtained through all three ways are consistent. This further validates the reliability of the photometric solutions when employing a single-band light curve.

Zoom In Zoom Out Reset image size

In addition to the above settings, several considerations were taken into account in determining the final modeling. First, the mass ratio was treated as a variable parameter, allowing for more accurate characterization of the systems. Then the third light (ℓ₃) was attempted for the potential of third bodies. However, because of the dense field of the stars, it was uncertain whether the observed third light was solely attributable to the third body. The final photometric solutions are listed in Table 3. In this table, a standardized definition was applied, where M₁ is the more massive one, the radii are set by the W-D fractional radii, r₁ and r₂ are the equivalent volume radii, and the semimajor axis is as given by the orbital period and estimated masses. The degree of contact is f = (Ω_in − Ω_star)/(Ω_in − Ω_out), where Ω_star is the modified dimensionless potential of the star surface, while Ω_in and Ω_out are the dimensionless potential of the inner and outer Roche lobe, respectively. The observed and theoretical light curves are displayed in Figure 4. The results show that these EBs are twin contact binaries, characterized by a mass ratio close to unity, high orbital inclination, and almost identical temperatures. Another interesting result is that they are almost deep-contact binaries, with a degree of contact (f) greater than 50%.

Zoom In Zoom Out Reset image size

Table 3. Photometric Solutions for Five Binaries

Parameters	S02776	S12878	S15994	S18865	S19959
q(M2/M1)	${0.97}_{-0.07}^{+0.03}$	${0.95}_{-0.1}^{+0.05}$	${0.97}_{-0.07}^{+0.03}$	${0.98}_{-0.08}^{+0.02}$	${0.93}_{-0.03}^{+0.07}$
i(°)	${88.1}_{-0.5}^{+1.9}$	${84.1}_{-1.5}^{+0.5}$	${83.7}_{-0.5}^{+0.5}$	${76.6}_{-0.5}^{+0.5}$	${89.7}_{-0.6}^{+0.3}$
T2/T1	${1.019}_{-0.005}^{+0.003}$	${0.999}_{-0.009}^{+0.001}$	${0.998}_{-0.003}^{+0.002}$	${0.998}_{-0.005}^{+0.002}$	${0.987}_{-0.004}^{+0.004}$
R2/R1	${0.99}_{-0.03}^{+0.01}$	${0.981}_{-0.031}^{+0.019}$	${0.99}_{-0.03}^{+0.01}$	${0.991}_{-0.031}^{+0.009}$	${0.968}_{-0.022}^{+0.032}$
r1	${0.449}_{-0.002}^{+0.010}$	${0.439}_{-0.006}^{+0.02}$	${0.438}_{-0.003}^{+0.012}$	${0.451}_{-0.014}^{+0.009}$	${0.413}_{-0.006}^{+0.006}$
r2	${0.444}_{-0.008}^{+0.003}$	${0.430}_{-0.008}^{+0.003}$	${0.433}_{-0.010}^{+0.002}$	${0.447}_{-0.009}^{+0.014}$	${0.400}_{-0.006}^{+0.006}$
ℓ1/(ℓ1 + ℓ2)(I)	${0.501}_{-0.001}^{+0.025}$	${0.510}_{-0.010}^{+0.015}$	${0.504}_{-0.004}^{+0.019}$	${0.504}_{-0.004}^{+0.016}$	${0.522}_{-0.022}^{+0.056}$
ℓ3(I%)	${14.9}_{-1.0}^{+1.5}$	${7.1}_{-4.0}^{+4.0}$	${19.0}_{-2.0}^{+2.0}$	${5.9}_{-3.0}^{+3.0}$	${0.6}_{-0.6}^{+1.4}$
ℓ1/(ℓ1 + ℓ2)(V)	⋯	⋯	⋯	${0.504}_{-0.004}^{+0.016}$	${0.523}_{-0.023}^{+0.056}$
ℓ3(V%)	⋯	⋯	⋯	${8.0}_{-3.0}^{+3.0}$	${0.6}_{-0.6}^{+1.4}$
f(%)	${64.0}_{-2.0}^{+4.2}$	${53.7}_{-6.0}^{+5.0}$	${55.4}_{-2.5}^{+5.5}$	${65.9}_{-5.0}^{+5.0}$	${27.9}_{-3.0}^{+3.0}$

Download table as:  ASCIITypeset image

According to the results of our investigation in the LMC, five twin contact binaries were detected out of 32 binaries, which were identified as massive contact binaries (they probably have B spectral types). The fraction of twin stars within this sample is 15.6% (5/32), which closely aligns with the estimated occurrence rate of twin binaries (∼10%) for this class of binaries given by Moe & Di Stefano (2017) and Offner et al. (2023) and helps to test the theory of these binaries evolving toward equal-mass pairs pointed by Menon et al. (2021) via the observations. Furthermore, these studies have also revealed that a significant majority of these binary systems (over 50%) have companions, including third bodies or even higher-order systems. This observation strongly suggests the presence of third bodies accompanying these twin binaries. This confirms the expected conclusions. The presence of such a high proportion of third bodies raises intriguing questions. One possible explanation is the influence of the massive binaries themselves since systems with higher component masses tend to have higher fractions of triple or higher-order systems. Another factor that could contribute to this phenomenon is the low-metallicity environment of the LMC, which is known to result in weaker stellar winds according to Yoon & Langer (2005). However, it is worth noting that Moe & Di Stefano (2013) found no statistically significant trends in metallicity between the Magellanic Clouds and the Milky Way. To gain a more comprehensive understanding, further investigations and studies are warranted in the future.

To obtain more information about third bodies, the following formula is used:

$$\begin{eqnarray}&&f(m)=\displaystyle \frac{{\left({M}_{3}\sin i\right)}^{3}}{{\left({M}_{1}+{M}_{2}+{M}_{3}\right)}^{2}}=\displaystyle \frac{4{\pi }^{2}}{{{GP}}_{3}^{2}}\times {\left({a}_{12}\sin i\right)}^{3},\end{eqnarray} \tag{ 3 }$$

where f(m) is the mass function of system, and M₁ is estimated via the temperature based on the online table (see footnote 7) by Mamajek. The value of M₁ was determined to be 4.7, 5.4, 9.0, 5.1, and 7.6 M_⊙ from S02776 to S19959, respectively. The mass of the secondary star (M₂), was calculated by the mass ratio q, while the minimum masses of the third bodies, M₃, range between 0.33 and 1.46 M_⊙. The maximum distances range from 6.7 to 11.4 au between the third bodies and the central binary systems. These results suggest the presence of low-mass third bodies with short orbital periods in the vicinity of these twin binaries. Remarkably, such close distances of these third bodies to the massive contact binaries, as compared to those documented by Li et al. (2022a), hint at specific mechanisms of stellar formation and evolution. These mechanisms may involve filament fragmentation, dense cores, and massive accretion disks, in agreement with the conclusions reached by Moe & Di Stefano (2017) and Offner et al. (2023), just as Tokovinin & Moe (2020) discussed the third bodies may also form because of the large gas reservoir for massive star formation.

Table 2 presents the positive $\dot{P}$ of three twins based on the O − C curves, while the other two are unchanged (S02776) and negative (S12878). When considering the trend of the parabolic curve caused by an orbital period change (no fourth body or more companions), this could be interpreted as mass transfer from the less massive component to the more massive one for a long-term period increase (S15994, S18865, and S19959) as they have already passed the stage of the shortest period (q = 1). While S12878 is experiencing a long-term period decrease, this could be the result of several factors, including mass transfer from the more massive star to the less massive one, angular momentum loss, or a combination of both. The situation for S02776 cannot be determined due to the limited time span of the observations. Therefore, mass transfer plays an important role for these twins, and they are classified as deep-contact binaries, except for S19959, based on the W-D method. A comparison with all massive binaries is described in Section 1, most of which are the deep-contact binaries (CT Tau, GU Mon, V701 Sco, V593 Cen, and M31V J00450522+4138462). Only VFTS 352 and HD 64315 are near the deep-contact status (30%), similar to S19959. All of them are potential progenitors of the double neutron star binaries proposed by Hwang et al. (2015). Furthermore, this evidence suggests that all the twin binaries in this study have evolved into contact binaries before reaching a mass ratio of unity and have filled the Roche lobes of both components during Case A mass transfer. The underlying causes of these phenomena warrant further investigation.

The presence of a third body is considered the most likely trigger for the observed phenomena. It is known that the metallicity of the LMC is lower than that of the Milky Way, which implies weak stellar winds (Yoon & Langer 2005) for these massive twin binaries. Based on the mechanisms for angular momentum transport (Kratter 2012), such as the magneto-rotational instability, disk winds, and gravitational torques, the reduced influence of stellar winds allows the third body to significantly influence the evolution of the inner binary through the eccentric Kozai–Lidov mechanism (Naoz & Fabrycky 2014; Naoz 2016). These oscillations can result in the transfer of angular momentum from the inner binary to the third body, leading to changes in the orbital period of the inner binary system. Tokovinin et al. (2006) have shown the detailed role of the third bodies in that most spectroscopic binaries with P < 3 days have a tertiary companion (see also Tokovinin 2020).

In summary, the study of these twin binaries in the LMC has provided several significant insights: (1) the detection of third bodies around all of these twins through LTTE suggests a remarkably high occurrence of such companions among massive binaries, potentially influenced by the metallicity of the LMC; (2) the presence of low-mass third bodies raises intriguing questions about their role in the formation and evolution of the massive binaries, which warrant further investigation; and (3) the third bodies may play a great role in facilitating the components of massive binaries to fill their Roche lobes and evolve into contact binaries in the LMC, which may occur during the Case A mass transfer. Overall, these results contribute to our understanding of the formation, evolution, and properties of twin binaries in a low-metallicity environment and shed light on the intriguing phenomena observed in these systems.

This work is partly supported by the Chinese Natural Science Foundation (grant Nos. 12303040, 11933008, and 11873017), the International Cooperation Projects of the National Key R&D Program (No. 2022YFE0127300) and the basic research project of Yunnan Province (grant Nos. 202001AT070091, and 202201AT070180). This paper makes use of online data (https://ogle.astrouw.edu.pl/) of OGLE and the observed data from MACHO (https://macho.nci.org.au) by the VizieR archives (https://vizier.cds.unistra.fr/viz-bin/VizieR). The authors thank the OGLE team and the MACHO team for making their observation data publicly available, which creates an opportunity for us to study the evolution of massive twin binaries in the LMC or other works.

The eclipse times of the five massive contact binaries are shown in Table 4, p and s are the primary and secondary minimum respectively.